To perform instance paired tracking, we design a matching strategy to track each paired shadow-object association across time frames following [1]}.
First, we assume \(N\)  instances in the tracking queue with their tracking embeddings represented by the features of each instance.
Then, we assume \(M\)  instances in the next video frame and compute their tracking embeddings.
Moreover, we obtain the similarity \(Score(f_i,f_j)\)  between the instances in the frame and the instances in the tracking queue by computing the cosine similarity of their tracking embeddings and normalizing via a bidirectional softmax function:
\(\begin{split}Score(f_i,f_j) = &[\frac{exp(cos(f_{i}, f_{j})) }{ {\textstyle \sum _{k=1}^{M}} exp(cos(f_{k}, f_{j}))}\\& + \frac{exp(cos(f_{i}, f_{j})) }{ {\textstyle \sum _{k=1}^{N}} exp(cos(f_{i}, f_{k}))}]/2 \ ,\end{split}\) 
